01 - Preheat the oven to 400°F.
02 - Place potatoes in a large pot of salted water and bring to a boil. Cook until fork-tender, approximately 15 minutes. Drain thoroughly and return to the pot. Mash with butter, warmed milk, salt, and pepper until smooth and creamy. Set aside.
03 - Heat olive oil in a large skillet over medium heat. Add chopped onion and sauté until softened and translucent, 3 to 4 minutes. Add minced garlic and cook for an additional minute until fragrant.
04 - Add ground beef to the skillet. Cook, breaking up the meat with a wooden spoon, until fully browned. Drain excess fat if necessary.
05 - Stir in tomato paste and all-purpose flour, cooking for 1 minute to remove raw flour taste. Gradually whisk in beef broth followed by Worcestershire sauce, dried thyme, and dried rosemary.
06 - Simmer the mixture for 5 minutes or until slightly thickened. Fold in frozen peas and carrots. Season with salt and pepper to taste. Remove from heat.
07 - Transfer the beef filling evenly into a 9x13-inch baking dish. Top with the mashed potatoes, spreading evenly with a spatula. Use a fork to create texture on the surface.
08 - Bake in the preheated oven for 20 minutes, or until the potato topping is golden brown and the filling is bubbling around the edges.
09 - Allow the Shepherd's Pie to rest for 5 minutes before serving to set the filling.